Hurts also threw for 153 yards and two touchdowns for the NFC-best Eagles, who moved to 10-1 for the fifth time in history. Miles Sanders ran for 143 yards and two scores as Philadelphia rushed for 363 overall, the second-best total for the franchise.
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Rodgers left in the third quarter with his team trailing 34-23 after grimacing his way through a drive that led to a Packers field goal. He had already been playing with a broken thumb and took several hard hits.
Rodgers' replacement, Jordan Love, kept the Packers (4-8) in the game by connecting with Christian Watson for a 63-yard catch-and-run touchdown that cut Philly's lead to 37-30.
But the Packers ran out of time against Hurts, who seems poised to take the torch from Rodgers as the next MVP.
Hurts had 254 combined yards, including 126 on the ground, and threw a TD pass in the first half as the Eagles built a 27-20 lead. He ripped off runs of 42, 28 and 24 yards.
In the second half, he hit A.J. Brown for a 6-yard TD pass and a 34-20 lead that just added to his staggering numbers on one of the great nights ever for an Eagles QB. Hurts topped Michael Vick's 130 yards rushing set in December 2010 against the New York Giants.
Rodgers was 11 of 16 passing for 140 yards, two touchdowns and two first-half interceptions.
Hurts put on a show in a lively first half that saw two Eagles get their first career picks and both teams miss an extra point while combining for seven touchdowns.
Bettors could have cashed in on the over in the first 30 minutes.
Philadelphia's high-octane offense had slowed of late - notably during the first loss of the season in the previous home game against Washington and last week's win over Indianapolis that needed a fourth-quarter rally - but Hurts put the Packers on notice with early rushes that would make an All-Pro running back envious. He ran for 52 yards on the opening drive and set up Kenneth Gainwell's 4-yard TD.
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Easy enough.
Then the game got wild. Rodgers had his second pass attempt batted by cornerback Darius Slay and snagged by Josiah Scott. Three plays later, Sanders scored on a 15-yard run. But Jake Elliott missed the PAT.
Rodgers led the Pack right back. A.J. Dillon scored on a 20-yard run, Rodgers hit Randall Cobb for an 11-yard score, and it was 14-13 late in the first quarter.
Hurts, though, closed the half with a 42-yard run and a 1-yard run, close enough to the end zone to set up Sanders' 2-yard scoring run on the first play of the second quarter.
Rodgers again came back and threw a 23-yard TD pass to Aaron Jones. Mason Crosby matched Elliott with a missed extra point and it was 20-20.
That was about all Rodgers could muster.
Hurts took it from there and threw a 30-yard TD pass to Quez Watkins - whose fumble against the Commanders played a pivotal role in the Eagles' lone defeat.
INJURIES
Packers: S Darnell Savage injured a foot.
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Eagles: C.J. Gardner-Johnson, the NFL interception leader with six, suffered a rib injury in the first half.
WINNING HISTORY
The Eagles won NFL championships after starting 10-1 in 1949 and 2017. The other times they did it, they lost the Super Bowl (1980, 2004).
RARE DUO
Hurts and Sanders became the first teammates to run for at least 125 yards apiece since San Francisco's Frank Gore (158) and Colin Kaepernick (151) on Dec. 20, 2014.
ALL-TIME GREATS
The Eagles inducted former defensive ends Hugh Douglas and Trent Cole into their Hall of Fame.
UP NEXT
Packers: At Chicago next Sunday.
Eagles: Host Tennessee next Sunday.